On the Significance of Digits in Interval Notation

TL;DR

This paper examines the importance of digits in interval notation using information theory, proposing more efficient representations that balance readability and information retention.

Contribution

It introduces an information-theoretic approach to evaluate and optimize the digit usage in interval bounds for improved clarity.

Findings

Quantifies information content of interval digits

Proposes a measure of digit efficiency

Suggests more readable interval presentations

Abstract

To analyse the significance of the digits used for interval bounds, we clarify the philosophical presuppositions of various interval notations. We use information theory to determine the information content of the last digit of the numeral used to denote the interval's bounds. This leads to the notion of efficiency of a decimal digit: the actual value as percentage of the maximal value of its information content. By taking this efficiency into account, many presentations of intervals can be made more readable at the expense of negligible loss of information.